Planarizing solutions including abrasive elements, and methods for manufacturing and using such planarizing solutions

ABSTRACT

A planarizing slurry for mechanical and/or chemical-mechanical polishing of microfeature workpieces. In one embodiment, the planarizing slurry comprises a liquid solution and a plurality of abrasive elements mixed in the liquid solution. The abrasive elements comprise a matrix material having a first hardness and a plurality of abrasive particles at least partially surrounded by the matrix material. The abrasive particles can have a second hardness independent of the first hardness of the matrix material. The second hardness, for example, can be greater than the first hardness. The matrix material can be formed into a core having an exterior surface and an interior. Because the abrasive particles are at least partially surrounded by the matrix material, the abrasive particles are at least partially embedded into the interior of the core.

TECHNICAL FIELD

The present invention relates to chemical-mechanical planarization of microfeature workpieces. Several aspects of the present invention are related to unique abrasive elements used in slurries for mechanical and/or chemical-mechanical polishing of microfeature workpieces on the planarizing surface of a polishing pad.

BACKGROUND

Mechanical and chemical-mechanical planarization (“CMP”) processes remove material from the surface of microfeature workpieces in the production of microelectronic devices and other products. FIG. 1 schematically illustrates a rotary CMP machine 10 with a platen 20, a carrier head 30, and a planarizing pad 40. The CMP machine 10 may also include an under-pad 50 between an upper surface 22 of the platen 20 and a lower surface of the planarizing pad 40. The under-pad 50 provides a thermal and mechanical interface between the planarizing pad, 40 and the platen 20. A drive assembly 26 rotates the platen 20 (indicated by arrow F) and/or reciprocates the platen 20 back and forth (indicated by arrow G). Since the planarizing pad 40 is attached to the under-pad 50, the planarizing pad 40 moves with the platen 20 during planarization.

The carrier head 30 has a lower surface 32 to which a microfeature workpiece 12 may be attached, or the workpiece 12 may be attached to a resilient pad 34 or bladder system. The carrier head 30 may be a weighted, free-floating wafer carrier, or an actuator assembly 31 may be attached to the carrier head 30 to impart rotational motion to the microfeature workpiece 12 (indicated by arrow J) and/or reciprocate the workpiece 12 back and forth (indicated by arrow I).

The planarizing pad 40 and a planarizing solution 44 define a planarizing medium that mechanically and/or chemically-mechanically removes material from the surface of the microfeature workpiece 12. The planarizing solution 44 may be a conventional CMP slurry with abrasive particles and chemicals that etch and/or oxidize the surface of the microfeature workpiece 12.

To planarize the microfeature workpiece 12 with the CMP machine 10, the carrier head 30 presses the workpiece 12 facedown against the planarizing pad 40. More specifically, the carrier head 30 generally presses the microfeature workpiece 12 against the planarizing solution 44 on a planarizing surface 42 of the planarizing pad 40, and the platen 20 and/or the carrier head 30 moves to rub the workpiece 12 against the planarizing surface 42. As the microfeature workpiece 12 rubs against the planarizing surface 42, the planarizing medium removes material from the face of the workpiece 12. The force generated by friction between the microfeature workpiece 12 and the planarizing medium will, at any given instant, be exerted across the surface of the workpiece 12 primarily in the direction of the relative movement between the workpiece 12 and the planarizing pad 40. The carrier head 30 can include a retaining ring 33 to counter this force and hold the microfeature workpiece 12 in position.

The CMP process must consistently and accurately produce a uniformly planar surface without defects on workpieces to enable precise fabrication of circuits and photo-patterns. A nonuniform surface can result, for example, when the removal rate of material is not uniform across the surface of the workpiece.

Defects in the form of voids, tear outs, indents, scratches or chatter marks can be caused by the interface between the workpiece, the planarizing solution, and the planarizing pad. The planarizing solution can greatly affect the nonuniformity in removal rates and the number of defects on a workpiece. For example, hard abrasive particles and/or large abrasive particles are a significant source of defects because they are more likely to cause scratches or other types of surface asperities on the workpiece. On the other hand, small particles have a very low polishing rate that is unacceptable in many applications, and small particles can also cause dishing because they are more likely to contact the inner portions of deep depressions on the workpiece. The problems associated with planarizing solutions are exacerbated as the feature sizes shrink because even slight defects and/or dishing can ruin such small features.

Composite Abrasive Slurries (CAS) show promising results in reducing defects and dishing. FIG. 2 schematically illustrates an existing CAS 44 that has been developed for CMP processing. The slurry 44 includes a liquid solution 60 and composite abrasive particles 70. The composite abrasive particles 70 have cores 72 with exterior surfaces 73 and a plurality of abrasive particles 74. The abrasive particles 74 are held to the exterior surface 73 of a core 72 by interaction forces, such as chemical bonding and/or electrical attraction forces. The cores 72 can be soft cores made from polymeric materials or hard cores made from large abrasive particles. In a soft core application, the composite abrasive particles 70 are formed by (a) forming polymeric microspheres without abrasive particles and then curing the microspheres to make the cores 72, (b) mixing the cores 72 and the abrasive particles 74 in a liquid solution such that the zeta potentials between the cores 72 and the abrasive particles 74 cause the particles 74 to be attracted to the exterior surfaces 73 of the cores 72, and (c) optionally chemically reacting the particles and polymer to form a chemical bond. The known composite abrasive particles 70 accordingly have abrasive particles 74 only on the exterior surfaces 73 of the cores 72.

Although the CAS 44 shown in FIG. 2 produces some desirable results, it also raises several problems for CMP processing. First, the composite abrasive particles 70 require very small abrasive particles 74 that are not readily available. This results in high material costs and requires complex manufacturing techniques to handle such particles. Second, the small abrasive particles 74 can be detached from the cores 72 because the interaction forces may not be sufficient to withstand the forces exerted against the composite abrasive particles 70 during a planarizing cycle. This results in a relatively slow polishing rate and dishing because the CAS 44 begins to act like a conventional CMP slurry with very small particles as more abrasive particles 74 become detached from the cores 72. Third, the liquid solution 60 and any cleaning solutions are limited to maintaining the zeta potentials between the cores 72 and the particles 74 so that the liquid solution 60 does not cause the cores 72 to repel the particles 74. This limits the composition of the cores 72 and the particles 74, and it also restricts the constituents of the planarizing solution. Therefore, existing CASs also have several problems and limitations. Similar limitations exist with mixed abrasive slurries in which different types of abrasive particles are mixed in a common solution.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic cross-sectional view of a planarizing system in accordance with a prior art.

FIG. 2 is a schematic cross-sectional view of a composite abrasive slurry in accordance with the prior art.

FIG. 3 is a schematic cross-sectional view of an abrasive element for a composite abrasive slurry in accordance with an embodiment of the invention.

FIG. 4 is a schematic cross-sectional view of an abrasive element for a composite abrasive slurry in accordance with another embodiment of the invention.

FIG. 5 is a schematic cross-sectional view of an abrasive element for a composite abrasive slurry in accordance with another embodiment of the invention.

FIG. 6 is a schematic cross-sectional view of an abrasive element for a composite abrasive slurry in accordance with another embodiment of the invention.

FIG. 7 is a schematic cross-sectional view of a planarizing system using a composite abrasive slurry in accordance with an embodiment of the invention.

FIG. 8 is a cross-sectional view showing a portion of the planarizing system of FIG. 7 in greater detail.

DETAILED DESCRIPTION

A. Overview

The present invention is directed to slurries, planarizing systems, and methods for mechanical and/or chemical-mechanical planarization of microfeature workpieces. The term “microfeature workpiece” is used throughout to include substrates in or on which microelectronic devices, micro-mechanical devices, data storage elements, and other features are fabricated. For example, microfeature workpieces can be semiconductor wafers, glass substrates, insulated substrates, or many other types of substrates. Furthermore, the terms “planarization” and “planarizing” mean either forming a planar surface and/or forming a smooth surface (e.g., “polishing”). Several specific details of the invention are set forth in the following description and in FIGS. 3-8 to provide a thorough understanding of certain embodiments of the invention. One skilled in the art, however, will understand that the present invention may have additional embodiments, or that other embodiments of the invention may be practiced without several of the specific features explained in the following description.

One aspect of the invention is directed to a planarizing slurry for mechanical and/or chemical-mechanical planarization of microfeature workpieces. In one embodiment, the planarizing slurry comprises a liquid solution and a plurality of abrasive elements mixed in the liquid solution. The abrasive elements comprise a matrix material having a first hardness and a plurality of abrasive particles at least partially within the matrix material. The matrix material can be formed into a core having an exterior surface and an interior. The abrasive particles can have a second hardness independent of the first hardness of the matrix material. The first and second hardnesses, for example, can be different from each other such that the first hardness is either greater or less than the second hardness. In several embodiments, the abrasive particles are at least partially surrounded by the matrix material such that the abrasive particles are at least partially embedded into the interior of the core.

Another aspect of the invention is a planarizing system for chemical-mechanical planarization of microfeature workpieces. In one embodiment, the planarizing system includes a support member, a planarizing pad on the support member, and a workpiece holder configured to releasably retain a microfeature workpiece relative to the planarizing pad. The planarizing system further includes a planarizing slurry disposed on a planarizing surface of the planarizing pad. The planarizing slurry can comprise a liquid solution and a plurality of abrasive elements mixed in the liquid solution. The abrasive elements can comprise a matrix material and a plurality of abrasive particles at least partially within and bonded to the matrix material. As explained above, the matrix material can have a first hardness, and the abrasive particles can have a second hardness independent of the first hardness of the matrix material.

Another aspect of the present invention is a method of processing a microfeature workpiece. In one embodiment, the method includes disposing a planarizing slurry on a planarizing surface. The planarizing slurry can comprise any of the foregoing embodiments of planarizing slurries. For example, the planarizing slurry can comprise a liquid solution and a plurality of abrasive elements including a matrix material having a first hardness and a plurality of abrasive particles at least partially within and bonded to the matrix material. The method further includes removing material from the workpiece with the abrasive elements.

Still another aspect of the present invention is a method of manufacturing a slurry for chemical-mechanical planarization of microfeature workpieces. In one embodiment, the method includes making a plurality of abrasive elements by (a) mixing a plurality of abrasive particles and a matrix material when the matrix material is in a flowable state, and (b) atomizing the mixture of the matrix material and the abrasive particles into microspheres or other shapes with embedded abrasive particles. The abrasive elements accordingly have a volume of the matrix material and a number of the abrasive particles at least partially embedded into the matrix material. The method further includes mixing the abrasive elements with a liquid solution to form the planarizing slurry. In another embodiment, the method of making the abrasive elements further includes curing the matrix material to harden the matrix material and further retain the abrasive particles.

B. Embodiments of Abrasive Elements and Planarizing Slurries

FIG. 3 is a schematic cross-sectional view illustrating an abrasive element 300 ire accordance with one embodiment of the invention. In this embodiment, the abrasive element 300 includes a matrix material 310 and a plurality of abrasive particles 320. The matrix material 310 defines a core or binder with an exterior surface 312, and the abrasive particles 320 are at least partially embedded into the interior of the matrix material 310. The abrasive particles 320 are not merely attached to the exterior surface 312 of the matrix material 310, but rather the abrasive particles 320 are at least partially surrounded by the matrix material 310. Several of the abrasive particles 320, for example, are at least partially contained within and bonded to the interior of the matrix material 310. Some of the abrasive particles 320 have bearing surfaces 322 projecting beyond the exterior surface 312 of the matrix material 310. The bearing surfaces 322 of these abrasive particles 320 provide the mechanical elements that abrade the workpieces. As shown in FIG. 3, several other abrasive particles 320 can be completely surrounded by the matrix material 310 such that these abrasive particles 320 do not have an exposed bearing surface.

The matrix material 310 is generally selected to be chemically compatible with a liquid solution with which the abrasive elements 300 are mixed to make a slurry. The matrix material 310 is also selected for its hardness or other physical properties for controlling the removal rate, mitigating defects, inhibiting dishing, or meeting other performance criteria. In one embodiment, the matrix material 310 is a polymer microsphere core in which the abrasive particles 320 are embedded. The matrix material 310, however, can be formed into cores having configurations other than microspheres and being composed of materials other than polymers. In general, the matrix material 310 should be formed into cores that are discrete particle-like elements with a size not greater than 50 μm and, more particularly, from approximately 0.1 μm to 10.0 μm. The discrete cores formed from the matrix material 310 are accordingly sized to be suspended or otherwise mixed in the liquid solution of the planarizing slurry. Suitable materials for the matrix material 310 include latex, such as an emulsion polymerization of dienes or dienes with styrene. Other suitable materials include styrene, urethane, butyl rubber, silicones, and polyethylene. Urethane, for example, may be beneficial because the hardness of the urethane microspheres can be controlled by controlling the degree of cross linking and the amount of abrasives or other solids in the urethane. Because butyl rubber is relatively soft, butyl rubber may be beneficial in applications where it is desirable for the matrix material to erode and expose interior abrasive particles.

The abrasive particles 320 are selected to have a hardness independent of the hardness of the matrix material 310. For example, the matrix material 310 can have a first hardness and the abrasive particles 320 can have a second hardness greater than the first hardness of the matrix material 310. In other embodiments, however, the second hardness can be less than or equal to the first hardness. Suitable materials for the abrasive particles 320 include aluminum oxide, cerium oxide, silica, alumina, coated silicon oxides, zirconium compounds, titanium compounds, and other abrasive materials suitable for planarizing microfeature workpieces. The abrasive particles can have a median size of approximately 1 nm to approximately 0.5 μm. In several embodiments, the abrasive elements have a median size of approximately 25 nm to 250 nm, and in certain embodiments from approximately 50 nm to approximately 100 nm.

The abrasive elements 300 can be configured to provide a desired polishing rate, inhibit dishing, and reduce defects. The polishing rate of the abrasive elements 300 can be controlled by the compositions of the matrix material and the abrasive particles, the percentage of abrasive particles by volume or by weight in the elements, and the size of the matrix material and/or the abrasive particles. In general, the abrasive elements 300 should be sufficiently hard to have a reasonable polishing rate without being so hard that they produce defects. The abrasive elements 300 can inhibit defects by having sufficiently small bearing surfaces 322 projecting from the matrix material 310 and/or a sufficiently elastic or deformable matrix material 310 to avoid scratching or producing other surface asperities on the workpiece. The size of the bearing surfaces 322 can be controlled by the size of the abrasive particles 320 and the extent that the outer abrasive particles 320 project beyond the matrix material 310. Additionally, dishing can be inhibited by having a sufficiently large overall size for the abrasive elements 300 and by embedding the abrasive particles 320 into the matrix material 310 so that they are not easily detached. The aspect of having a composite abrasive element 300 with embedded abrasive particles 320 enables a wide range of options to achieve a sufficiently high polishing rate without creating unacceptable defects and dishing. Thus, several embodiments of the abrasive elements 300 provide significant advantages over existing composite abrasive slurries and other types of slurries, as explained below.

One advantage of several embodiments of the abrasive element 300 shown in FIG. 3 is that the embedded abrasive particles 320 are not as likely to be detached from the matrix material 310 compared to the composite abrasive particles shown in FIG. 2. Embedding the abrasive particles 320 within the matrix material 310 provides a strong bond between the abrasive particles 320 and the matrix material 310. This allows the abrasive elements 300 to be used in a wider range of solutions because the pH of the solution is not limited by the zeta potentials of the abrasive particles 320 and the matrix material 310. As such, a broad range of matrix materials can be used in a broad range of planarizing solutions and cleaning solutions to provide very good results for both planarizing and cleaning workpieces. Also, because only the bearing surfaces 322 of the abrasive particles 320 are exposed to the workpieces, the abrasive elements 300 can have larger abrasive particles 320 than existing CAS slurries that have particles only on the exterior surface of the core. This allows the abrasive elements to use less expensive, larger particles to reduce the costs of the slurry without producing defects normally associated with larger particles. Moreover, embedding the abrasive particles 320 into the matrix material 310 is expected to provide a more consistent polishing rate throughout a planarizing cycle because the abrasive particles 320 stay attached to the matrix material 310 during a planarizing cycle. The aggregate surface area of abrasive particles 320 exposed to the workpiece is expected to remain reasonably consistent throughout a planarizing cycle.

Another advantage of several embodiments of the abrasive elements 300 is that they do not produce dishing. The overall size of the abrasive elements 300 is sufficiently large to prevent removal of material from deep within depressions on the workpiece. Also, because the abrasive particles 320 are securely bonded to the matrix material 310, the abrasive particles 320 do not become detached from the matrix material 310. Therefore, the abrasive elements 300 are also expected to reduce dishing in CMP processes.

Yet other advantages of several embodiments of the abrasive elements 300 are that they produce a high polishing rate with abrasive surfaces that do not produce defects. Several embodiments of the abrasive elements 300 thus provide the benefits of a high polishing rate with low defects while mitigating dishing.

FIG. 4 is a schematic cross-sectional view illustrating an abrasive element 400 in accordance with another embodiment of the invention. In this embodiment, the abrasive element 400 includes a matrix material 410 defining a core, a plurality of first abrasive particles 420, and a plurality of second particles 430. The first abrasive particles 420 are at least partially embedded into the matrix material 410 such that they are at least partially within the matrix material 410. The second particles 430 can also be embedded into the matrix material 410, but in some embodiments the second particles 430 can be surface particles 440 that are merely attached to the exterior surface of the matrix material 410.

The first abrasive particles 420 can be composed of a first material and the second particles 430 can be composed of second material different from the first material. In another embodiment, the first abrasive particles 420 can have a first size and the second particles 430 can have a second size different from the first size. The first abrasive particles 420 and the second particles 430, for example, are not limited to being composed of different materials; rather, they may have different median sizes but be composed of the same material. It will be appreciated that at least one property of the first abrasive particles 420, such as the size, composition, shape, hardness, etc., is different from a property of the second particles 430.

Several embodiments of the abrasive elements 400 may provide desirable planarizing characteristics to the planarizing slurry. For example, the first abrasive particles 420 can be one type of an abrasive and the second particles 430 can be another type of an abrasive. The abrasive elements 400 can provide such results because embedding the particles 420 and 430 into the matrix material 410 enables much more flexibility in selecting materials for the abrasive elements compared to existing composite abrasive particles that are limited to materials and liquid solutions which provide the correct zeta potentials.

FIG. 5 is a schematic cross-sectional view illustrating an abrasive element 500 in accordance with yet another embodiment of the invention. In this embodiment, the abrasive element 500 includes a matrix material 510 and relatively large abrasive particles 520 at least partially embedded within the matrix material 510. The abrasive element 500 accordingly illustrates that the overall size of the abrasive element 500 can remain substantially the same as abrasive elements 300 and 400, but that the abrasive particles can be much larger to reduce dishing on the surface of a workpiece and avoid using costly small particles.

FIG. 6 is a schematic cross-sectional view illustrating an abrasive element 600 in accordance with another embodiment of the invention. In this embodiment, the abrasive element 600 includes an inner part 602, a matrix material 610 surrounding the inner part 602, and a plurality of abrasive particles 620 at least partially embedded into the matrix material 610. The inner part 602 can be a relatively inexpensive material, or it can be selected to provide a desired hardness or size to the abrasive element 600. The abrasive element 600 may be particularly useful for producing large abrasive elements because the inner element 602 can be sized to increase the overall element size. The abrasive element 600 can also be particularly useful to reduce the amount of matrix material 610 and/or abrasive particles 620 that are used to form the abrasive element 600 for reducing material costs.

The abrasive elements 300, 400 and 500 illustrated in FIGS. 3-5, respectively, can be formed by mixing the abrasive particles with the matrix material while the matrix material is in a flowable state. In the case of polymeric matrix materials, for example, the abrasive particles can be mixed with a polymer melt. In general, the mixture of the matrix material and the abrasive particles is approximately 10%-99% matrix material by volume with approximately 1%-90% abrasive particles by volume. In other embodiments, the composition can have approximately 60%-90% matrix material by volume and approximately 10%-40% abrasive particles by volume. The individual abrasive elements can then be formed by emulsion polymerization, spray drying, or heterogeneous polymerization techniques. After the individual abrasive elements are formed, the polymeric matrix material can be cured or otherwise hardened in an optional process to securely bind the abrasive particles to the matrix material. In another optional process, part of the cured matrix material can then be dissolved to expose more of the bearing surfaces of the outer abrasive particles. Such erosion of the matrix material can accordingly optimize the abrasiveness of the abrasive elements.

Another advantage of several embodiments of the abrasive elements illustrated above with respect to FIGS. 3-5 is that they are relatively simple to manufacture. Because the solid abrasive particles can be mixed with the polymer melt before forming the abrasive elements, it is possible to precisely control the distribution of the abrasive particles within the abrasive elements. This is also expected to provide good control of the hardness and abrasiveness of the abrasive elements.

The abrasive element 600 shown in FIG. 6 can be made by mixing the abrasive particles 620 with the matrix material 610 while the matrix material 610 is in a flowable state. The inner part 602 can then be coated with the flowable mixture of matrix material 610 and abrasive particles 620. The matrix material 610 can be cured in an optional procedure after coating the inner part 602.

C. Embodiments of Planarizing Systems and Methods of Processing Workpieces

FIG. 7 is a schematic cross-sectional view illustrating a planarizing system 700 for planarizing a microfeature workpiece W using planarizing slurries with abrasive elements in accordance with an embodiment of the invention. The planarizing system 700 can include a support member 702, such as a platen, and a drive assembly 704 coupled to the support member 702 to rotate and/or translate the support member 702. The planarizing system 700 further includes a subpad 706 on the support member 702 and a planarizing pad 708 on the subpad 706. The planarizing pad 708 has a planarizing surface 709 configured to engage the workpiece W. The planarizing system 700 further includes a carrier assembly 710 having a workpiece holder 712 and an actuator 714 coupled to the workpiece holder 712. The actuator 714 moves the workpiece holder 712 to (a) raise and lower the workpiece W relative to the planarizing pad 708, and (b) rotate and/or translate the workpiece holder 712 relative to the planarizing surface 709.

The planarizing system 700 further includes a slurry supply 720 containing a planarizing slurry 730 in accordance with an embodiment of the invention. For example, the planarizing slurry 730 can include a liquid solution 732 and a plurality of abrasive elements 734 suspended or otherwise mixed in the liquid solution 732. The abrasive elements 734 can be any of the embodiments of abrasive elements 300, 400, 500, and 600 described above. The slurry supply 720 dispenses the planarizing slurry 730 onto the planarizing surface 709 of the planarizing pad 708 (shown schematically).

FIG. 8 is a cross-sectional view illustrating a portion of the planarizing system 700 of FIG. 7 in greater detail. Referring to FIG. 8, the planarizing slurry 730 typically covers the planarizing surface 709 of the planarizing pad 708. In operation, a method of planarizing a microfeature workpiece accordingly comprises disposing the planarizing slurry 730 onto the planarizing surface 709 such that a plurality of the abrasive elements 734 and the liquid solution 732 contact the workpiece Was the support member 702 and/or the workpiece holder 712 move relative to each other. The abrasive elements 734 accordingly remove material from the surface of the workpiece W.

From the foregoing, it will be appreciated that specific embodiments of the invention have been described herein for purposes of illustration, but that various modifications may be made without deviating from the spirit and scope of the invention. Accordingly, the invention is not limited except as by the appended claims. cm 1-32. (canceled) 

33. A method of manufacturing a slurry for chemical-mechanical planarization of microfeature workpieces, the method comprising: mixing a plurality of abrasive particles and a matrix material when the matrix material is in a flowable state; atomizing the mixture of the matrix material and the abrasive particles into small units defining discrete abrasive elements, wherein the abrasive elements have a volume of the matrix material and at least a number of the abrasive particles partially embedded into the matrix material; and mixing the abrasive elements with a liquid solution.
 34. The method of claim 33, further comprising modifying a property of the abrasive elements after atomizing the mixture.
 35. The method of claim 33 wherein mixing a plurality of abrasive particles and a matrix material includes mixing (a) a maxtrix material comprising a polymer, and (b) a plurality of abrasive particles comprising aluminum oxide, alumina, silicon oxide, coated silicon oxides, silica, cerium oxide, zirconium compounds, and/or titanium compounds.
 36. The method of claim 33 wherein: mixing a plurality of abrasive particles and a matrix material includes mixing the plurality of abrasive particles with a matrix material comprising a polymer; and atomizing the mixture of the matrix material and the abrasive particles into small units defining discrete abrasive elements includes forming abrasive elements with the volume of the matrix material having a size not greater than 50 μm.
 37. The method of claim 33 wherein atomizing the mixture of the matrix material and the abrasive particles into small units defining discrete abrasive elements includes forming abrasive elements with (a) the volume of the matrix material having a size from approximately 0.1 μm to 10.0 μm, and (b) the abrasive particles having a median size from approximately 1 nm to approximately 0.5 μm.
 38. The method of claim 33 wherein mixing a plurality of abrasive particles and a matrix material includes mixing a matrix material comprising a polymer with a plurality of first abrasive particles having a first composition and a plurality of second abrasive particles having a second composition different than the first composition.
 39. The method of claim 33 wherein atomizing the mixture of the matrix material and the abrasive particles into small units defining discrete abrasive elements includes forming abrasive elements with the volume of the matrix material having a first material at the center and a second material coating the first material, and wherein the abrasive particles are partially embedded into the second material. 